Multi-objective Optimisation of Building Geometry for Energy Consumption and View Quality

Multi-objective Optimisation of Building Geometry forEnergy Consumption and View Quality

Zack Xuereb Conti1, Paul Shepherd2, Paul Richens31Singapore University of Technology & Design 2,3University of [email protected] [email protected]@cantab.net

In property development, the view quality contributes significantly to the propertyvalue. In many cases, the architect is constrained by the property developer totake full advantage of the view by designing large glazed facades ignoring theconsequence on the energy consumption of the building caused by the conflictingorientation of the view. This paper presents a design tool to help the architectinteractively explore different building and window geometries that trade-offenergy consumption (kWh) and view quality (€). This design tool allowsinteraction with parametric building geometry, simulation of energy consumptionand view quality, and an optimisation search engine. The simulation of the viewquality quantifies a view according to the visibility and quality of its contents byusing a novel view-scoring method. The design tool is tested with bothnorth-oriented and south-oriented views and produces a Pareto front from whichresulting geometries are visualised.

Keywords: Optimisation, Simulation, Energy consumption, View quality, Designtool

INTRODUCTIONIn recent years, Mediterranean towns have seen agrowing trend of old seafront houses being replacedwith luxury apartment blocks. In most cases, the ar-chitect is constrained by the property developer todesign large glazed facades to gain full visibility ofthe seafront, which raises the property value. Thisapproach, however, ignores the implications on thecooling load of the building caused by the orienta-tion of the view.

This study proposes an interactive design tool al-lowing the architect to search for trade-off solutionsbetween a profit-yielding view quality and a reduced

cooling load. The approach can be broken down intothe parametrisation of the building geometry, thethermal and view quality analysis, and subsequentoptimisation. These aspects were combined into anintegrated software application.

EA-BASED DESIGNTo the author's knowledge, there is no existing liter-ature dealing explicitly with view quality in the con-text of low energy optimisation of buildings despitethe optimisation of daylight and heat transfer beingcommonly researched through two approaches; theoptimisation of the fenestrations alone (Shea et al.

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2006; Wright andMourshed 2009; Gagne and Ander-sen 2010; Wright et al. 2013) and the optimisationof the envelope together with fenestrations (Bouch-laghem 2000; Caldas and Norford 2002; 2003). Theseall propose a form of design tool coupling simula-tion and optimisation methods. Caldas & Norford(2002; 2003) employ Pareto optimisation using a Ge-netic Algorithm (GA) to search for solutions thatmax-imise the useful daylight and minimise heating re-quirements. Bouchlaghem (2000) presents a com-puter model which simulates thermal performancetaking into account design variables related to thebuilding's envelope and fabric and applies numeri-cal optimisation techniques to automatically deter-mine the optimum design variables, which achievethe best thermal comfort conditions. Efforts by Sheaet al. (2006) also focus on maximising lighting per-formance andminimising cost of building envelopesby subdividing the envelope into a number of pan-els whereby each panel can take one of four differentopacities. They coupled a Multi-criteria Ant ColonyOptimisation (MACO) algorithm with daylight simu-lation computed in 'Radiance'. Data for each panelwas precompiled and used as an input into the opti-misation algorithm, so that the lighting calculationswere performed once. Similarly, Wright & Mour-shed (2009) adopt the cellular subdivision methodto achieve an almost free-form fenestration geom-etry. However, the subdivision approach was com-putationally expensive due to large number of vari-ables. The energy use of each solutionwas simulatedexternally in 'EnergyPlus' (Crawley et al. 2000). A bi-nary encoded GA was employed as the optimisationsearch. This approach was applied further to a multi-objective problem to minimise energy consumptionand construction costs (Wright et al. 2013), usingDebet al.'s (2002)Non-dominatedSortingGeneticAl-gorithm II (NSGA-II) for its efficiency in dealing withmulti-objective problems of this nature. The build-ing energy-use (kWh) accounted for the annual heat-ing, coolingandelectrical usewhile the capital cost ofthe facade was calculated by accounting for the con-struction cost of the opaque and glazed cells and for

overhangs. Gagne & Andersen's method (2010) al-lows the user to input a 3D massing model and per-formance target goals of illuminance and glare. Anexternal simulation engine 'Lightsolve Viewer' (An-dersen et al. 2008) was used together with a GA.

The simulation in nearly all of these approacheswas performed in available commercial softwarepackages. The research outlined in this paper em-phasises on simplified energy calculations for quickvisual feedback during the interactive early stagesof design. The proposed design tool has an in-builtreal-time simulation of solar radiation and fenestra-tion shading, which together contribute to the cal-culation of the cooling load objective function mea-sured in Kilo Watt Hours (kWh).

PROBLEM SET-UPThe geometry under study is representative of thecontext of this research. A parametricmodel of a reg-ular block of apartments was modelled. The param-eters considered include building-site dimensions,number of floors, tilt angle of facades, numberofwin-dows, overhang, etc.

While, the significant reduction in solar radiationcaused by overhangs or externalmechanical shadingdevices has been widely researched, their architec-tural design value comes across as a late design so-lution when not considered at the early stages of thedesign process. This paper focuses on improving theenergy-use of the building purely by self-shading ge-ometry. The use of external shading devices are alsoa deterrent to the view quality if they are visible. Onthe other hand, the use of internal blinds obstructsthe view and contradict the design intent for largeglazing. This research explores the effects of cast-ing shadows on thewindows below (see left in figure1) and of tilting the facade about the horizontal axisof the facade, to produce a larger angle of solar inci-dence (see right in figure 1), as ameans to reduce theenergy consumption. These objectives dictated thechoice of variables to produce overhangs and tilt thefacade.

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Figure 1Shaded windows(left), tiltedwindows (right).

An approach to wall fenestration such as Wright &Mourshed's cellular approach (2009) is applicable tothe problem being considered. However it involves alarge number of variables which slow down the opti-misation. Therefore, a more geometrical method us-ing fewvariables todefine thewindowgeometrywasadopted. The method allows window arrangementsranging from fully glazed walls to multiple individualwindowswhose height andwidth canbe individuallycontrolled.

SIMULATIONMETHODSThermalThe thermal objective is being defined as the con-sumption load (kWh) required to cool a building ina Mediterranean climate. It is assumed that thecooling load is required only during the peak sum-mer months since the worst case for the conflict be-tween the energy consumption and the orientationof the view is during the warm months. A numberof calculation methods were reviewed including theCooling Load Temperature DifferenceMethod (CLTD)(ASHRAE 1979), the Cooling Degree Days method(Day et al. 2000), the LT method (Baker and Steemers1996) and the Admittance method (CIBSE 2006).

The latter method was selected for implemen-tation in the design tool because the pre calculatedcooling load values it makes use of, can be calcu-lated (see equation 3). This was important in orderto avoid storing large sets of tabulated values intothe design tool. These values refer to the coolingload caused by heat gain through a window. Theglobal solar radiation ISG is determined from theknowledgeof the orientation andposition of the sun,which the design tool is capable of calculating. The

total cooling load (see formula 3) accounts for theheat gain (QW ) through the unshadowed area of thewindow (ATGlazing) (see formula1) and theheatgain(QQ+fRoof) through theunshadowedarea (ATRoof)of the roofs in the case of terraced floors (see formula2). Consumption loads due to casual gains were ig-nored for faster calculations at early design stage.

QW = UGlazingATGlazing[TE − TR]+

FCISG

(1)

QQ+Roof = URoofAT Roof[(TSAmean−TR) + (TSA − TSAmean)]

(2)

QT = QW +QQ+fRoof (3)

Where:UGlazing is the U-Value of the glazing is the areaURoof is the U-Value of the roof materialTE is the external ambient temperatureTR is the internal dry bulb base temperatureFC is the air-node coefficient (CIBSE guide)ISG is the global solar radiationTSAmean is the mean sol-air temperatureTSA is the sol-air temperature

Figure 2Dynamicsubdivision andshadow raytracingof windows.


The projected shadows cast on the windows are de-termined bymeans of a recursive subdivision routinewhere at each division, the window vertices are ray-traced to test for intersectionwith the overhung floorabove (see figure 2). For each subdivided face, theradiation is calculated and accumulated, resulting inthe total heat gain through the unshaded area of thewindow.

ViewQualityView quality is regarded to be a subjective matter.However for optimisation, the view quality needssome form of objective function. Whilst there havenot been any known attempts at the quantificationof the quality of the view in the context of an op-timisation problem, Shellard (2006) reviews a num-ber of attempts in evaluating a view for real-estatepurposes using hedonic regression to decomposethe constituent characteristics of the property value(Lake et al. 1998, Yu et al. 2007). The view qual-ity in the real-estate sector is somehow rationalisedandobjectively rated. This indicates that agoodqual-ity view can indeed be distinguished from an inferiorquality view. After consulting with a property realtor,the view types were categorised into a discrete setof direct sea view, direct country view, side sea view,side country view, open views (such as town squaresand townscapes) and no view at all.

Figure 3An example of agood view (left) andan inferior view(right), in real-estateterms.This research adopts a simplified hedonic approach

by sampling a set of properties of known floor areas,within a luxury condominium. A condominiumoffersconsistency for comparison, since contributing fac-tors such as location, amenities, etc are the same. Themain varying factors are the floor areas and the viewquality. Therefore, the aim is to derive a value persquare metre, for the view component of the prop-erty rental value (€/month/m2) for a coherent com-parison between different floor areas. This is done

by extracting it from the property valuemarketed bythe property agent. After consulting with a projectmanager of the condominium, the properties facingthe best view, were originally valued at double thosewith the 'worst' view. This assumption was used todeduct the the view component from the propertyvalue to determine the value of the floor area only.

Two apartments in the condominium with ex-treme view types (direct sea view and no view) werecompared and resulted that the values for their floorarea only, compared well when eliminating the viewcomponent of the direct sea view apartment, thusconfirming the project manager's assumption. Theaverage monthly value for the floor area only was€10.56/month/m2. This ratewas then applied to anapartment of different area with side sea views. Themonthly value for the floor area (€10.56×330m2)was subtracted from the market rental value of thisapartment (€5,500/month), resulting in the value ofthe view component (€2015.2/month), which whendivided by the area, compares well with the viewcomponent of the other properties as it lies midwaybetween the direct sea view whose monthly viewvalue rate was €10.6/month/m2 and the no view.The results seem to indicate linear variation betweenthe view type and their derived monthly view value(€/month/m2), for this particular location. The de-rived monthly floor area and view values were thenapplied to other properties in the same town, butnot within the same condominium, and their result-ing property values also compared well with the val-ues marketed by the property agents, thus confirm-ing the reliability of the derived monthly view valuerate for this particular study.

The property agent's categorising of the viewquality assumes a uniform view as it does not qual-ify the view based on its specific contents.

This simplification called for a smartermethod ofassessing the view quality by developing a scoringsystem whereby a window score represents the totalof the individually and appropriately scored 'items'in the view. A 'pixel-scoring' method was developedwithin the design tool whereby eachwindowwas as-


signed a score based on the total score from 4 differ-ent viewing positions on the corresponding floor.

Figure 4Colour-scoring onunwrapped imageof panoramic view.

A score range is represented by 255 greyscale toneswhere: 0 [black] = 6 points, 50 = 5 points, 87 = 4points, 162 = 3 points, 209 = 2 points, 255 [white]= 1 point. The user is asked to mark up the 360deg image based on their subjective judgement us-ing these colours (see figure 4). The condominiumapartment with the best view discussed earlier andand whose monthly rent is €6000 and monthly viewvalue €3000, is used as an example. The view visiblefrom its fully glazed facadewas simulated and scored2480764 points. One scored point was determinedto be equivalent to €0.00121 by dividing the score bythe monthly view value. The same exercise was re-peated for a side sea-view, view type and this scored1991232 corresponding to a monthly view value of€2,408. As expected it is lower than the direct seaview value.

Figure 5 presents amodel used to score the viewthrough awindow. This is based onmapping the 360degrees colour-scored panoramic image of the viewshown in Figure 4, onto the circumference of a cylin-der of infinite radius, since the objects in the view arerelatively far away from the observer. Therefore, thisassumes parallelism between the vectors ~A and ~B(see figure 5). These assumptions however, cause vi-sual inaccuracieswhendisplaying theboundaryA'B'because the geometry with an assumed infinite ra-dius is being visualised in perspective, using finitedimensions. The field of vision (FOV) from the ob-server's position ~E, through the windowAB, is pro-jected as a region, onto the mapped image on thecylinder. The pixels within that projected region are

scored and counted. The horizontal field of vision(hFOV ) and the vertical field of vision (vFOV ) arefound trigonometrically using vectors ~A and ~B tode-termine the indices of the pixels within region A'B'.This approachalso takes view-obstructingoverhangsinto account. The obstructed pixels are scored only 1point.

Figure 5Geometrical modelto determineprojected windowboundary onto thewrapped image.

OPTIMISATION APPROACHThe idea of implementing an optimisation algorithmis to search the design space for geometries that re-duce energy consumption yet yield high view value,which at times can conflict, depending on the orien-tation of the building and the direction of the sun.

The use of Evolutionary Algorithms (EA) inmulti-objective optimisation have been well documentedby Coello et al. (2007). Genetic Algorithms (GA)are a common type of EA adapted and applied tomulti-objective optimisation. GAs are founded ona population-based evolutionary approach, whichsearch for different areas in the solution space si-


multaneously. The Non-dominated Sorting GeneticAlgorithm-II (NSGA- II) (Deb et al. 2002) and theStrength Pareto Evolutionary Algorithm 2 (SPEA-2)(Zitzler et al. 2001) are common approaches. A goodoverview of the application of GA in multi-objectiveoptimisation was given by Deb (2001) and more re-cently by Konak et al. (2006).

This research implements the NSGA-II (Deb,Pratap et al. 2002) which performed well for sim-ilar optimisation problems (Wright, Brownlee et al.2013). This is a GA based search method that em-ploys elitism. Elitism ensures that the best solutionsof a generation are retained for the next generationand replaced only if they become dominated. Thisalso ensures cheaper computation. An initial popula-tion is randomly generated and offsprings are gener-ated by crossing over and mutating the parent pop-ulation. The parent and child population are thencombined and sorted by comparing each solution tothe rest of the combined set and assigning a rank in-dex corresponding to the number of other solutionsthey are dominated by. A rank index of zero corre-sponds to a Pareto solution as it is not dominated byany other solution.

A visualisation of the optimisation was devel-oped within the design tool allowing the user toview the solutions, identify the colour coded Paretofront, and view the corresponding geometries andvalues, when interacting with the solutions (see fig-ure 6). The usermay easily choose to constrain or un-constrain variables during the optimisation. The usermay also select the population size, the number of it-erations and the mutation factor by which the non-constrained variable values will mutate and withinthe range of each respective variable. Solutions frompast generations are plotted in white and their age isrepresented by their transparency. This visualises theevolution of the solutions fromonegeneration to thenext. The view value lies on the y-axis and has beeninverted in order to visualise a more familiar Paretocurve, whilst the cooling load lies on the x-axis.

The software application was built in an objectoriented approach to benefit from the reuse of cer-

tain complex routines such as the shadow raytracing,window subdivision and cooling load calculation.The variables controlling the geometry of the apart-ment block were represented as a group of slider ob-jects (ControlP5) and written as an object represent-ing the DNA of a solution. The software was built en-tirely in Processing (Fry and C.Reas 2004). Figure 6 vi-sualises the user interface.

Figure 6Interaction withplotted Paretosolutions tovisualise thecorrespondinggeometry in themain viewport.

RESULTSPareto analyses were performed with two objectivefunctions: minimising energy consumption requiredto cool an apartment building and maximising theview quality visible through the windows. Two caseswere investigated; one with the desirable view to thenorth and the other to the south. In either case, apopulation size of 450 was used and run for 5 gen-erations. Figures 7 and 8 visualise the resulting non-dominated Pareto front and corresponding geome-tries of each study. The terracing, facade tilts, num-ber of windows, and window dimensions were al-lowed to vary in only one direction whilst keepingthedimensions of the building site fixed to simulate atypical sandwiched building footprint. In both cases,


the history of the evolution of the solutions is visu-alised by more transpearent points. The view valueon the y-axis has been inverted in order to visualisea more familiar Pareto curve meaning that solutionstowards the origin are fitter in both objectives.

In both cases, solutions A to E lie on the Paretofront (F1) as they are not dominated by any other so-lution while F, G and H lie on the second front (F2),meaning they are each dominated by one solution.

Study1:.As expected, solutionA (see figure 7) showsthat a large glazed facade produces excellent viewquality and a decent cooling load since the view ori-entation avoids the direct solar beam for most of theday. Heat gain from diffused radiation is the con-tributing component to the cooling load in this case.Solutions E and F (see figure 7) clearly visualise thedirect relationship between the window size and thecooling load, and the view quality. Overall, it can beseen that thewindow size is the dominant parameterdriving the optimisation.

Study 2:. Despite Solution A (see figure 8) not prov-ing the hypothesis of reducing the cooling load bytilting the facade, it is interesting to point out that so-lution C (see figure 8) indicates that casting shadowson the windows has a larger effect on improving thecooling load. This also indicates that a positive tilt,consequently producing an overhung floor, is moredominant than the negative tilt. Interestingly, Solu-tion D (see figure 8) achieves an improved coolingload due to a combination of a higher solar incidenceangle (negative facade tilt) and narrow yet tall win-dows still producing a decent view quality.

It can be seen in both studies that besides con-tributing to the cooling load, the dimensions of thefloor plan also have an inverse relationship with theview quality since the view is sampled from 4 differ-ent positions on the floor plan. The visibility of theview deteriorates when viewed from deeper withinthe room.

The generation of the initial population seemedto have influence on the variety of solutions (Wrightand Mourshed 2009). However this study used nor-mally distributed random variables since the focus

was not to improve the algorithm but to develop adesign tool.

Figure 7Study 1: Resultingfronts (left),correspondinggeometries (right).

Figure 8Study 2: Resultingfronts (left),correspondinggeometries (right).

CONCLUSIONThis research presents a design tool to help an archi-tect interactively explore different building and win-dow geometries that trade-off the energy consump-tion and view quality. The energy consumption issimulated in the design tool using real-time calcula-tions of solar radiation based on location and time.The view is simulated, and its quality is quantified us-ing a real-estate approach and abespoke scoring sys-tem. Finally, the design tool makes use of a GA (Debet al. 2002) as a search optimisation method.

The simulation methods developed, coupledwith a Pareto-optimal approach, were able to createa variety of architectural shapes characterised by ter-racing and inclination of faces, that responded to de-sign objectives for reduced energy consumption andincreased view quality. The results from the Pareto-based studies provide valuable information in under-standing the trade-offs between the conflicting ob-jectives. It suggested that increasing the angle of so-


lar incidenceby tilting the facade, has less of an effectthan casting shadows on the windows.

Introducing design variables such as facade tiltand over hung floors in the optimisation, producednew ways to reduce the energy consumption as op-posed to only varying the window size. The explo-ration of newdesign variables is non trivial because itis limited to the user's intuitiveness and understand-ing of the problem. However the use of such an ex-ploration tool allows the user to get one step closerby understanding the relationship between the un-commonly compared objectives. This is not limitedto iterative exploration of the design space but alsoencourages to use the design tool as a manual 'hillclimbing' exercise.

The element of interaction in the proposed andfuture improved version of the design tool searchesto bridge the gap between the use of such a compu-tational solution-search paradigm and smaller, per-haps more traditional firms that employ a more ana-logue approach.

REFERENCESAndersen, M, Yi, L, Kleindienst, S, Lee, J, Bodart, Magali

and Cutler, B 2008, 'An intuitive daylighting perfor-mance analysis andoptimization approach', BuildingResearch and Information : the international journalof research, development and demonstration, 36(6),pp. 593-607

ASHRAE, initials missing 1979, Cooling and heating loadcalculationmanual., ASHRAE, Atlanta, Georgia

Baker, N andSteemers, K 1996, 'LTMethod3.0—a strate-gic energy-design tool for Southern Europe', Energyand Buildings, 23(3), pp. 251-256

Bouchlaghem, N 2000, 'Optimising the design of build-ing envelopes for thermal performance',Automationin Construction, 10(1), pp. 101-112

Caldas, LG and Norford, LK 2002, 'A design optimizationtool based on a genetic algorithm', Automation inConstruction, 11(2), pp. 173-184

Caldas, L and Norford, L 2003, 'Shape Generation UsingPareto Genetic Algorithms: Integrating ConflictingDesignObjectives in Low-EnergyArchitecture', Inter-national Journal of Architectural Computing, 1(4), pp.503-515

CIBSE, initialsmissing 2006, CIBSEGuideA: Environmental

Design, CIBSECoello, CAC, Lamont, GB and Van Veldhuisen, DA 2007,

Evolutionary algorithms for solving multi-objectiveproblems, Springer

Crawley, D B, Pedersen, CO, Lawrie, L K andWinkelmann,F C 2000, 'EnergyPlus: Energy Simulation Program(2000)', ASHRAE Journal, 42(4), pp. 49-56

Deb, K 2001,Multi-objective optimizationusing evolution-ary algorithms, John Wiley & Sons

Deb, K, Pratap, A, Agarwal, S and Meyarivan, T 2002,'A fast and elitist multiobjective genetic algorithm:NSGA-II', Evolutionary Computation, IEEE Transac-tions on, 6(2), pp. 182-197

Gagne, JML and Andersen, M 2010 'Multi-Objective Fa-cade Optimization for Daylighting Design Using aGenetic Algorithm', SimBuild 2010, New York

Konak, A, Coit, DW and Smith, AE 2006, 'Multi-objectiveoptimization using genetic algorithms: A tutorial',Reliability Engineering \& System Safety, 91(9), pp.992-1007

Lake, IR, Lovett, AA, Bateman, IJ and Langford, IH 1998,'Modelling environmental influences on propertyprices in anurban environment', Computers, Environ-ment and Urban Systems, 22(2), pp. 121-136

Shea, K, Sedgwick, A and Antonuntto, G 2006, 'Multi-criteria Optimization of Paneled Building EnvelopesUsing Ant Colony Optimization', in Smith, IC (eds)2006, Intelligent Computing in Engineering andArchi-tecture, Springer Berlin Heidelberg, pp. 627-636

Shellard, J 2006 'Modelling Dimensions of Height andView at Melbourne', University of Auckland, NewZealand, Pacific Rim Real Estate Society 12th AnnualConference

Wright, JA, Brownlee, AEI, Mourshed, MM and Wang, M2013, 'Multi-objective optimization of cellular fen-estration by an evolutionary algorithm', Journal ofBuilding Performance Simulation, 7, pp. 1-19

Yu, SM, Han, SS and Chai, CH 2007, 'Modeling the valueof view in high-rise apartments: a 3D GIS approach',Environment and Planning B: Planning and Design,34(1), pp. 139-153

Zitzler, E, Laumanns, M and Thiele, L 2001 'EvolutionaryMethods for Design, Optimization and Control WithApplications to Industrial Problems', Proc. EUROGEN2001, Athens, Greece


Multi-objective Optimisation of Building Geometry for Energy Consumption and View Quality

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